Classifying edge-biregular maps of negative prime Euler characteristic

Introducing edge-biregular maps

We introduce the concept of alternate-edge-colourings for maps, and study highly symmetric examples of such maps. Edge-biregular maps of type $(k,l)$ occur as smooth normal quotients of a particular index two subgroup of $T_{k,l}$, the full triangle group describing regular plane $(k,l)$-tessellations. The resulting colour-preserving automorphism groups can be generated by four involutions. We explore special cases when the usual four generators are not distinct involutions, with constructions relating these maps to fully regular maps. We classify edge-biregular maps when the supporting surfac…

欧拉示性数为-1的曲面上PL $d$-流形的半等角宝石的分类

A classification of semi-equivelar gems of PL $d$-manifolds on the surface with Euler characteristic $-1$

本文对欧拉示性数为-1的曲面上PL d-流形的半等角宝石进行分类，证明了其类型限于12种特定度数序列，并给出存在性构造。

正则图的分类：具有欧拉特征数$-p^4$的正则图分类

A classification of regular maps with Euler characteristic $-p^4$ for a prime $p\geq 5$

本文研究了欧拉特征数为$-p^4$的正则图，证明了其Sylow $p$-子群的阶数限制，并分类了所有此类正则图，表明当$p$不在{2,3,5,7,13}时，相关曲面不支持正则图。